Size dependence of the disruption threshold: laboratory examination of millimeter–centimeter porous targets

Abstract

The outcome of collision between small solid bodies is characterized by the threshold energy density Q⁎s, the specific energy to shatter, that is defined as the ratio of projectile kinetic energy to the target mass (or the sum of target and projectile) needed to produce the largest intact fragment that contains one half the target mass. It is indicated theoretically and by numerical simulations that the disruption threshold Q⁎s decreases with target size in strength-dominated regime. The tendency was confirmed by laboratory impact experiments using non-porous rock targets (Housen and Holsapple, 1999; Nagaoka et al., 2014).In this study, we performed low-velocity impact disruption experiments on porous gypsum targets with porosity of 65–69% and of three different sizes to examine the size dependence of the disruption threshold for porous material. The gypsum specimens were shown to have a weaker volume dependence on static tensile strength than do the non-porous rocks. The disruption threshold had also a weaker dependence on size scale as Q⁎s∝D−γ,γ≤0.25−0.26, while the previous laboratory studies showed γ=0.40 for the non-porous rocks. The measurements at low-velocity lead to a value of about 100Jkg−1 for Q⁎s which is roughly one order of magnitude lower than the value of Q⁎s for the gypsum targets of 65% porosity but impacted by projectiles with higher velocities. Such a clear dependence on the impact velocity was also shown by previous studies of gypsum targets with porosity of 50%.